SCEN103 Midterm Exam

April 7, 1999

1. (2 pts.)
Two lamps A and B of identical resistance are connected in series to a battery having negligible internal resistance - each lamp glows with the same intensity. Lamp A is suddenly shorted out by connecting a wire across its terminals. Specify as completely as possible what happens to the intensity of each lamp.

2. (4 pts.)
Much of the copper wiring in your home is probably 12 gauge (a measure of its diameter), which has about 0.005 ohm of resistance for each meter of length. If a 20 A circuit is constantly used at its full capacity, estimate the monthly cost of the energy lost to heating in the wiring.

3. (4 pts.)
A circuit rated for 20 A is being used to operate a toaster (1000 W) and a lamp (100 W). When a 1500 W hairdryer is run on the same circuit with the other devices, the circuit breaker opens the circuit to avoid overheating of the household wiring. For quickest drying of hair, the maximum possible rating for the hairdryer is desired. Would you recommend purchasing a 1200 W hairdryer, or should a lower power 1000 W unit be acquired?

4. (6 pts.)

Consider the following circuit that represents a small penlight, one alkaline AAA cell connected to a lamp. The AAA cell provides 1.5 V and has an internal resistance r of 0.6 ohms. The lamp resistance R may be assumed to be 7.0 ohms. What is the current through the lamp? What is the terminal voltage of the AAA cell? How much of the battery’s power is wasted by its internal resistance?

5. (4 pts.)
Your friend is having trouble starting an old car. Eager to apply your new expertise with circuits, you decide to determine the internal resistance of the battery to see if a new 12 V battery is needed. You phone your physics instructor, widely known for his generosity, and borrow a digital multimeter. You also borrow a 10 ohm resistor since you recall that the battery must be loaded to measure the effects of internal resistance, observed by connecting the resistor to the battery and measuring the change in the battery's terminal voltage.

What power should the resistor be able to dissipate adequately to conduct this test successfully? Arriving back at the car, you discover that unfortunately the voltmeter mode of the multimeter has been damaged. However the ammeter mode still seems to be working so you rig the circuit shown. A current of 1.10 A is measured with the meter. What is the internal resistance of the battery?